Problem: Carbon- $14$ is an element that loses about $10\%$ of its mass every millennium (i.e., $1000$ years). A sample of Carbon- $14$ has $600$ grams. Write a function that gives the sample's mass in grams, $S(t)$, $t$ millennia from today. $S(t)=$
Explanation: Losing mass at a rate of $10\%$ per millennium means the sample keeps $100\%-10\%=90\%$ of its mass each millennium. So each millennium, the size is multiplied by $90\%$, which is the same as a factor of $0.9$. If we start with the initial mass, $600$ grams, and keep multiplying by $0.9$, this function gives us the mass of the sample $t$ millennia from now: $S(t)=600(0.9)^t$